Charline von Heyl is a leading contemporary painter with no signature style. That's confusing. Or at least it is if you're inclined to think of artists as brands. There is tremendous pressure on emerging artists to settle on a signature style. It reassures lazy curators and collectors, for one thing. It also fosters the illusion that an artist is delving deeper and deeper into a kind of creative essence.

But there's peril in consistency. "Know thyself" may be wise counsel. But perhaps we need to accept the extent to which we are not, in fact, knowable; nor are we necessarily one thing. It follows that we should refuse to let any single expression of ourselves snuff out all the other possibilities. The tendency toward distilled aesthetic consistency has plagued abstract art in particular. To contemplate a career like Mark Rothko's or Jackson Pollock's is to sense not just the aesthetic limitations of a signature style, but also certain psychic dangers.

Von Heyl, 58, whose large-scale abstract works - bravura, moody and mysterious - are now on view in an exultant show at the Hirshhorn Museum, avoids all that. Like such contemporary painters as Thomas Nozkowski, Amy Sillman and Laura Owens, Von Heyl refuses to let one idea about what painting should be predominate.

There is nothing programmatic about how the German artist - who divides her time between New York and Marfa, Texas - works. Everything is up for discussion in the executive boardroom of her painterly intelligence. Nothing is settled. Everything is in doubt, and hesitation is a creative lubricant, expanding her field of vision.

In an interview in the exhibition catalogue, von Heyl speaks about "the atmosphere" of each of her paintings. She looks at a work in progress and thinks about "how aggressive or defensive it is, how deep it goes into possible anecdote, and how much there's seduction or refusal."

These characterizations are a reminder that abstract paintings, far from being esoteric, are often most fruitfully contemplated in straightforward human terms. Von Heyl's paintings are (if you'll indulge an unlikely extended metaphor) like the college-age cousin who comes from overseas to stay in your house while you're still in high school. She has a weird sense of fashion, she broods in her room, she upends the domestic dynamic - yet she has just enough life experience to charm and intimidate your school friends. She's sort of there and not there, seductive yet alienating. You wisely keep your distance, but you're desperate to know her secrets.

"Lady Moth," which von Heyl painted last year, holds its secrets particularly close. The artist sets curving, asymmetrical shapes over black diagrammatic lines and a white ground, horizontally lined with what look like musical staves. Most of the curving shapes are in a brushy blue acrylic, gorgeously diluted and smudged with ghosted marks. But there's one that's symmetrical, filled in with soft black charcoal and marked like a death's-head hawkmoth. The light and texture of the wing against the graphic decorative effects around it haunts the painting with a morbid intimacy.

"Lady Moth" was painted after the artist's mother died. We learn from the wall label that both mother and daughter shared a fondness for wordplay - hence moth/mother. But you don't need to know this: The painting has already drawn you in, and connected you with a world beyond it.

"I'm just trying to keep the paintings ahead of language," von Heyl says in the catalogue. "Or better yet, ahead of sentences." She is eager, she continues, to "move past definitions and on to something more personal and fragile, a place where thoughts and feelings meet, where looking feels like thinking."

"Manna Hatta" is one of the standouts in the show of more than 30 paintings. Overlapping translucent patterns cut in and out apparently at random: concentric circles, waves, Ben-Day dots and black-and-white patterns that teeter on the cusp of forming an M.C. Escher illusion. Yet all of this somehow coheres to form the shape of a head in profile

Three cartoonlike rabbits frolic across the painting's lower part. The rabbits, filled in with red Ben-Day dots, may be a nod to Sigmar Polke's 1966 painting "Bunnies" (Playboy bunnies in his case, but also rendered in dots). The title, "Mana Hatta," calls to mind the urban industry addressed in Walt Whitman's poem "Mannahatta," and a 1921 film by Paul Strand and Charles Sheeler, "Manhatta."

But again, none of this particularly matters. Sure, it's instructive that von Heyl loves allusions and wordplay. But trying to explain the meaning of her work in these terms alone is futile. Her word games are just one more layer in a complex confection that is primarily visual, sometimes philosophical and always generative.

Wild and expressive as von Heyl's paintings can often appear, they also tap into the sober-seeming spirit of Jasper Johns's influential injunction: "Take an object. Do something to it. Do something else to it." In fact, von Heyl's fondness for building up her pictures with textures, colors, patterns and shapes can make her seem more like a printmaker than a painter. "It's a constant juggling of different layers, speeds, and materials," she says. "There is no way to explain it all. It's ... a lot of bringing forward and pushing back, and a lot of different tools producing different stories."

All in all, this brilliant show reminds us how much life there is in looking, feeling and thinking through paint. Belief in most of the 20th century's rationales for abstraction is a guttering flame. But von Heyl doesn't worry about that. She picks up her tools. She accepts the precariousness of her plight. And she paints.